%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM435+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:10 PM UTC 2026
% Result : Theorem 0.15s 1.30s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 65 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 77 ( 37 ~; 29 |; 9 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0,X1,X2] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f12,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f23,axiom,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& xp != sz00
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__979) ).
fof(f25,axiom,
( aInteger0(xm)
& sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1032) ).
fof(f26,conjecture,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f27,negated_conjecture,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(flattening,[],[f27]) ).
fof(f39,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f40,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f42,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(flattening,[],[f41]) ).
fof(f57,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f23]) ).
fof(f59,plain,
aInteger0(xp),
inference(cnf_transformation,[],[f23]) ).
fof(f63,plain,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)),
inference(cnf_transformation,[],[f25]) ).
fof(f64,plain,
aInteger0(xm),
inference(cnf_transformation,[],[f25]) ).
fof(f65,plain,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f28]) ).
fof(f73,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f74,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f185,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X1,sdtasdt0(X0,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(superposition,[],[f74,f73]) ).
fof(f209,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X1,sdtasdt0(X0,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aInteger0(X2) ),
inference(duplicate_literal_removal,[],[f185]) ).
fof(f2941,plain,
( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm))
| ~ aInteger0(xq)
| ~ aInteger0(xp)
| ~ aInteger0(xm) ),
inference(superposition,[],[f63,f209]) ).
fof(f3028,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xp)
| ~ aInteger0(xm) ),
inference(forward_subsumption_resolution,[],[f2941,f65]) ).
fof(f3070,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xm) ),
inference(forward_subsumption_resolution,[],[f3028,f57]) ).
fof(f3083,plain,
~ aInteger0(xm),
inference(forward_subsumption_resolution,[],[f3070,f59]) ).
fof(f3085,plain,
$false,
inference(forward_subsumption_resolution,[],[f3083,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM435+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n007.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 19:51:55 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/1.30 % (1741242)Detected formulas, will run a generic FOF schedule.
% 0.15/1.30 % (1741247)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=332907058:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.15/1.30 % (1741253)dis-21_1_sil=8000:lcm=predicate:random_seed=2055578106:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.15/1.30 % (1741250)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=187878493:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.15/1.30 % (1741251)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=12855996:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.15/1.30 % (1741252)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1648926234:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.15/1.30 % (1741248)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1747035248:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.15/1.30 % (1741249)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=770082140:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.15/1.30 % (1741253)Refutation not found, incomplete strategy
% 0.15/1.30 % (1741253)------------------------------
% 0.15/1.30 % (1741253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.30 % (1741253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.30 % (1741253)CaDiCaL version: 2.1.3
% 0.15/1.30 % (1741253)Termination reason: Refutation not found, incomplete strategy
% 0.15/1.30 % (1741253)Time elapsed: 0.005 s
% 0.15/1.30 % (1741253)Peak memory usage: 88 MB
% 0.15/1.30 % (1741253)Instructions burned: 6 (million)
% 0.15/1.30 % (1741251)First to succeed.
% 0.15/1.30 % (1741251)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1741242"
% 0.15/1.30 % (1741252)Instruction limit reached!
% 0.15/1.30 % (1741252)------------------------------
% 0.15/1.30 % (1741252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.30 % (1741252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.30 % (1741252)CaDiCaL version: 2.1.3
% 0.15/1.30 % (1741252)Termination reason: Instruction limit
% 0.15/1.30 % (1741252)Termination phase: Saturation
% 0.15/1.30 % (1741252)Time elapsed: 0.048 s
% 0.15/1.30 % (1741252)Peak memory usage: 90 MB
% 0.15/1.30 % (1741252)Instructions burned: 142 (million)
% 0.15/1.30 % (1741250)Instruction limit reached!
% 0.15/1.30 % (1741250)------------------------------
% 0.15/1.30 % (1741250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.30 % (1741250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.30 % (1741250)CaDiCaL version: 2.1.3
% 0.15/1.30 % (1741250)Termination reason: Instruction limit
% 0.15/1.30 % (1741250)Termination phase: Saturation
% 0.15/1.30 % (1741250)Time elapsed: 0.067 s
% 0.15/1.30 % (1741250)Peak memory usage: 89 MB
% 0.15/1.30 % (1741250)Instructions burned: 110 (million)
% 0.15/1.30 % (1741261)lrs+10_1_sil=8000:sp=occurrence:random_seed=3989357183:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.15/1.30 % (1741262)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2700996203:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.15/1.30 % (1741253)------------------------------
% 0.15/1.30 % (1741253)------------------------------
% 0.15/1.30 % (1741261)Instruction limit reached!
% 0.15/1.30 % (1741261)------------------------------
% 0.15/1.30 % (1741261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.30 % (1741261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.30 % (1741261)CaDiCaL version: 2.1.3
% 0.15/1.30 % (1741261)Termination reason: Instruction limit
% 0.15/1.30 % (1741261)Termination phase: Saturation
% 0.15/1.30 % (1741261)Time elapsed: 0.087 s
% 0.15/1.30 % (1741261)Peak memory usage: 93 MB
% 0.15/1.30 % (1741261)Instructions burned: 287 (million)
% 0.15/1.30 % (1741251)Refutation found. Thanks to Tanya!
% 0.15/1.30 % SZS status Theorem for theBenchmark
% 0.15/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.30 % (1741251)------------------------------
% 0.15/1.30 % (1741251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.30 % (1741251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.30 % (1741251)CaDiCaL version: 2.1.3
% 0.15/1.30 % (1741251)Termination reason: Refutation
% 0.15/1.30 % (1741251)Time elapsed: 0.043 s
% 0.15/1.30 % (1741251)Peak memory usage: 88 MB
% 0.15/1.30 % (1741251)Instructions burned: 74 (million)
% 0.15/1.30 % (1741251)------------------------------
% 0.15/1.30 % (1741251)------------------------------
% 0.15/1.30 % (1741242)Success in time 0.471 s
% 0.15/1.30 % Vampire exiting
%------------------------------------------------------------------------------